One implication of the unending nature of the interpretation of appearances through infinite sequences of signs is that Peirce can be no type of epistemological foundationalist or believer in absolute or apodeictic knowledge.

Logic, or Analytic, as the theory or method of arriving at true or apodeictic conclusions; and (2) Dialectic as the method of arriving at conclusions that are accepted or pass current as true, [Greek: endoxa] probabilia; conclusions in regard to which it is not taken for granted that they are false, and also not taken for granted that they are true in themselves, since that is not the point.

It is understood that a combination of assertory or of apodeictic premises may warrant an assertory or an apodeictic conclusion; but that if we combine either of these with a problematic premise our conclusion becomes problematic; whilst the combination of two problematic premises gives a conclusion less certain than either.

When we add further that, unless we deny that the notion of morality has any truth or reference to any possible object, we must admit that its law must be valid, not merely for men but for all rational creatures generally, not merely under certain contingent conditions or with exceptions but with absolute necessity, then it is clear that no experience could enable us to infer even the possibility of such apodeictic laws.